text: Another widely cited characteristic of gene regulatory network is their abundance of certain repetitive sub-networks known as network motifs. Network motifs can be regarded as repetitive topological patterns when dividing a big network into small blocks. Previous analysis found several types of motifs that appeared more often in gene regulatory networks than in randomly generated networks. As an example, one such motif is called feed-forward loops, which consist three nodes. This motif is the most abundant among all possible motifs made up of three nodes, as is shown in the gene regulatory networks of fly, nematode, and human.
  The enriched motifs have been proposed to follow convergent evolution, suggesting they are "optimal designs" for certain regulatory purposes. For example, modeling shows that feed-forward loops are able to coordinate the change in node A (in terms of concentration and activity) and the expression dynamics of node C, creating different input-output behaviors. The galactose utilization system of E. coli contains a feed-forward loop which accelerates the activation of galactose utilization operon galETK, potentially facilitating the metabolic transition to galactose when glucose is depleted. The feed-forward loop in the arabinose utilization systems of E.coli delays the activation of arabinose catabolism operon and transporters, potentially avoiding unnecessary metabolic transition due to temporary fluctuations in upstream signaling pathways. Similarly in the Wnt signaling pathway of Xenopus, the feed-forward loop acts as a fold-change detector that responses to the fold change, rather than the absolute change, in the level of β-catenin, potentially increasing the resistance to fluctuations in β-catenin levels. Following the convergent evolution hypothesis, the enrichment of feed-forward loops would be an adaptation for fast response and noise resistance. A recent research found that yeast grown in an environment of constant glucose developed mutations in glucose signaling pathways and growth regulation pathway, suggesting regulatory components responding to environmental changes are dispensable under constant environment.
  On the other hand, some researchers hypothesize that the enrichment of network motifs is non-adaptive. In other words, gene regulatory networks can evolve to a similar structure without the specific selection on the proposed input-output behavior. Support for this hypothesis often comes from computational simulations. For example, fluctuations in the abundance of feed-forward loops in a model that simulates the evolution of gene regulatory networks by randomly rewiring nodes may suggest that the enrichment of feed-forward loops is a side-effect of evolution. In another model of gene regulator networks evolution, the ratio of the frequencies of gene duplication and gene deletion show great influence on network topology: certain ratios lead to the enrichment of feed-forward loops and create networks that show features of hierarchical scale free networks. De novo evolution of coherent type 1 feed-forward loops has been demonstrated computationally in response to selection for their hypothesized function of filtering out a short spurious signal, supporting adaptive evolution, but for non-idealized noise, a dynamics-based system of feed-forward regulation with different topology was instead favored.